Yes, but only if you have some connection to the tartan (or if it's one that doesn't belong to a particular family or organization). E.g. I wear a MacKay tartan and a New Brunswick tartan (because I live in New Brunswick -- the Canadian province), but not a Royal Canadian Air Force tartan, nice as it is, because I'm not in the air force. I guess I would look at them as being similar to regimental or school ties.

^School and regimental ties I take seriously and respect. Since the whole business of proprietary "clan tartans" was cooked up by a couple of English charlatans early in the Victorian era, I will wear whatever tartan strikes my fancy, be it as a shirt, necktie or whatever. I would not wear a kilt in a clan tartan, but then I don't wear kilts, period.

Tartan ties are perfectly fine for work. I work in a conservative field (finance) and do not feel at all self conscious pairing a tartan tie with a suit for work or to a client meeting. I also don't care whose clan it is I am wearing. If someone wants to come after me with a claymore for this transgression, bring em on.